Robust control of nonlinear uncertain systems without generalized matching conditions

A novel procedure, called recursive-interlacing procedure, is proposed for designing globally stabilizing robust control. The procedure introduces new interlacing steps and combines them with the existing recursive or backstepping design. It is shown by examining all possible third-order vector systems that the procedure is applicable to systems not satisfying any of the existing structural conditions, that is, to systems in which uncertainties are potentially anywhere and of any bounding function. By its nature, the procedure is not limited to systems of any specific order; it either produces stabilizing control or reveals certain measure of unstabilizability, and it includes recursive design as a special case. >

[1]  S. Gutman.  Uncertain dynamical systems--A Lyapunov min-max approach , 1979 .

[2]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[3]  George Leitmann,et al.  On ultimate boundedness control of uncertain systems in the absence of matching assumptions , 1982 .

[4]  G. Leitmann,et al.  Robustness of uncertain systems in the absence of matching assumptions , 1987 .

[5]  Y. H. Chen,et al.  On the Robustness of Mismatched Uncertain Dynamical Systems , 1987 .

[6]  K. Wei.  Quadratic stabilizability of linear systems with structural independent time-varying uncertainties , 1990 .

[7]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[8]  Z. Qu,et al.  Robust Control of Generalized Dynamic Systems Without the Matching Conditions , 1991 .

[9]  Z. Qu.  Global stabilization of nonlinear systems with a class of unmatched uncertainties , 1992 .

[10]  Z. Qu.  Robust control of a class of nonlinear uncertain systems , 1992 .

[11]  A. Teel.  Using Saturation to Stabilize a Class of Single-Input Partially Linear Composite Systems , 1992 .

[12]  J. Slotine,et al.  Robust input-output feedback linearization , 1993 .

[13]  Riccardo Marino,et al.  Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, , 1993, Autom..

[14]  Zhihua Qu,et al.  Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions , 1993, 1993 American Control Conference.

[15]  Zhihua Qu,et al.  Robust control of cascaded and individually feedback linearizable nonlinear systems , 1994, Autom..